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Kostouraki A, Hajage D, Rachet B, Williamson EJ, Chauvet G, Belot A, Leyrat C. On variance estimation of the inverse probability-of-treatment weighting estimator: A tutorial for different types of propensity score weights. Stat Med 2024; 43:2672-2694. [PMID: 38622063 DOI: 10.1002/sim.10078] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/17/2023] [Revised: 02/12/2024] [Accepted: 04/01/2024] [Indexed: 04/17/2024]
Abstract
Propensity score methods, such as inverse probability-of-treatment weighting (IPTW), have been increasingly used for covariate balancing in both observational studies and randomized trials, allowing the control of both systematic and chance imbalances. Approaches using IPTW are based on two steps: (i) estimation of the individual propensity scores (PS), and (ii) estimation of the treatment effect by applying PS weights. Thus, a variance estimator that accounts for both steps is crucial for correct inference. Using a variance estimator which ignores the first step leads to overestimated variance when the estimand is the average treatment effect (ATE), and to under or overestimated estimates when targeting the average treatment effect on the treated (ATT). In this article, we emphasize the importance of using an IPTW variance estimator that correctly considers the uncertainty in PS estimation. We present a comprehensive tutorial to obtain unbiased variance estimates, by proposing and applying a unifying formula for different types of PS weights (ATE, ATT, matching and overlap weights). This can be derived either via the linearization approach or M-estimation. Extensive R code is provided along with the corresponding large-sample theory. We perform simulation studies to illustrate the behavior of the estimators under different treatment and outcome prevalences and demonstrate appropriate behavior of the analytical variance estimator. We also use a reproducible analysis of observational lung cancer data as an illustrative example, estimating the effect of receiving a PET-CT scan on the receipt of surgery.
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Affiliation(s)
- Andriana Kostouraki
- Inequalities in Cancer Outcomes Network, Department of Non-Communicable Disease Epidemiology, Faculty of Epidemiology and Population Health, London School of Hygiene and Tropical Medicine, London, UK
| | - David Hajage
- Département de Santé Publique, Centre de Pharmacoépidémiologie (Cephepi), CIC-1901, Sorbonne Université, Inserm, Institut Pierre-Louis d'Epidémiologie et de Santé Publique, AP-HP, Hôpital Pitié-Salpêtrière, Paris, France
| | - Bernard Rachet
- Inequalities in Cancer Outcomes Network, Department of Non-Communicable Disease Epidemiology, Faculty of Epidemiology and Population Health, London School of Hygiene and Tropical Medicine, London, UK
| | - Elizabeth J Williamson
- Department of Medical Statistics, Faculty of Epidemiology and Population Health, London School of Hygiene and Tropical Medicine, London, UK
| | | | - Aurélien Belot
- Inequalities in Cancer Outcomes Network, Department of Non-Communicable Disease Epidemiology, Faculty of Epidemiology and Population Health, London School of Hygiene and Tropical Medicine, London, UK
| | - Clémence Leyrat
- Department of Medical Statistics, Faculty of Epidemiology and Population Health, London School of Hygiene and Tropical Medicine, London, UK
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Wei K, Qin G, Zhang J, Sui X. Multiply robust estimation of the average treatment effect with missing outcomes. J STAT COMPUT SIM 2022. [DOI: 10.1080/00949655.2022.2143501] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/25/2022]
Affiliation(s)
- Kecheng Wei
- Department of Biostatistics, School of Public Health, and The Key Laboratory of Public Health Safety of Ministry of Education, Fudan University, Shanghai, People's Republic of China
| | - Guoyou Qin
- Department of Biostatistics, School of Public Health, and The Key Laboratory of Public Health Safety of Ministry of Education, Fudan University, Shanghai, People's Republic of China
- Shanghai Institute of Infectious Disease and Biosecurity, Shanghai, People's Republic of China
| | - Jiajia Zhang
- Department of Epidemiology and Biostatistics, University of South Carolina, Columbia, SC, USA
| | - Xuemei Sui
- Department of Exercise Science, University of South Carolina, Columbia, SC, USA
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